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Japanese Journal of Applied Physics

Basic study on linear optical quantum computers with liquid crystal devices

Satoshi Yokotsuka, Hiroyuki Okada

Published Oct 12, 2023• 6 citations
Publisher

Abstract

Abstract A basic experiment on 2-bit quantum calculations related to the Deutsch–Jozsa algorithm on a linear optical quantum computer using a liquid crystal (LC) device as a linear optical element was investigated. By controlling the phase of each of the two split laser beams and checking the number of photons at the output, it is possible to determine if the input bits are “not equal” or “not uniform.” The phase of the laser light was controlled using an LC device and a half-wave plate, and changes in the interference state of the output light and the number of photons were observed. The voltage application to the LC device is set at the input bit. As a result, the interference state changed according to the input bit, and changes in the number of photons were observed.

DOI
10.35848/1347-4065/ad02a7

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Abstract A basic experiment on 2-bit quantum calculations related to the Deutsch–Jozsa algorithm on a linear optical quantum computer using a liquid crystal (LC) device as a linear optical element was investigated. By controlling the phase of each of the two split laser beams and checking the number of photons at the output, it is possible to determine if the input bits are “not equal” or “not uniform.” The phase of the laser light was controlled using an LC device and a half-wave plate, and changes in the interference state of the output light and the number of photons were observed. The voltage application to the LC device is set at the input bit. As a result, the interference state changed according to the input bit, and changes in the number of photons were observed.
We review recent research in various types of optical quantum computing using liquid crystal devices. First, we have investigated Young’s Interference experiment using self-aligned liquid crystal (LC) devices and a logical “NOT” operation is achieved. Second, numerical quantization of interfering small photons using an LC retarder is investigated. Third, a Mach–Zehnder interferometer with an optical phase control by a twisted nematic (TN) LC device was studied. Fourth, a basic experiment on 2-bit quantum calculations related to the Deutsch-Jozsa algorithm on a linear optical quantum computer using the LC device as a linear optical element was investigated.
Four-bit input linear quantum computing with liquid crystal (LC) devices was studied using the Deutsch–Jozsa algorithm. A laser beam is split into four paths and passed through a configuration of twisted nematic (TN) LC device/(λ/2 waveplate)/TN LC device for computation. In order to minimize the effect of photon loss in the light path, a 4 × 4 matrix analysis was done for optimization. We fabricated a prototype for four optical-path linear quantum computing. As a result, we obtained changes in the number of photons counting according to Deutsch–Jozsa’s algorithm under the extremely weak light state.
We review recent research in various types of optical quantum computing using liquid crystal (LC) devices. First, we have investigated Young's Interference experiment using self-aligned LC devices and a logical “NOT” operation is achieved. Second, numerical quantization of interfering small photons using a LC retarder is investigated. Third, a Mach-Zehnder interferometer with an optical phase control by a twisted nematic (TN) LC device was studied. Fourth, 4-bit optical path linear quantum computation using Deutsch-Jozsa algorithm with the LC device as a linear optical element was investigated.
Abstract In efforts toward the realization of quantum computers, there have been many proposals to implement controlled NOT gates between quantum bits (qubits). However, the number of quanta in the experimentally realized system has been at most two. Because it is difficult to cope with both the realization of the conditional interaction (e.g., huge nonlinear interaction) between the quanta, and the maintenance of quantum coherence for a sufficient time, the realization of quantum logic gates using several quanta may be difficult in the near future. In this paper, a new method which implements a quantum algorithm using linear optics and single photons is described. This method does not need any huge nonlinearity. Hence, it is practical with today's technology and will be one of the useful physical test beds for the quantum algorithms. The optical implementation of the Deutsch–Jozsa algorithm with a 4‐bit input is proposed, and the mechanism is explained. As one instance of the recent progress of our project, an experiment of single‐photon interference using parametric fluorescence with highly stabilized interferometer system is reported. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(11): 52–60, 2001
Abstract Numerical quantization of interfering small photons using a liquid crystal (LC) retarder is investigated. A beam splitter can be considered a four-port device with the input-output relations in the Heisenberg picture using the creation and annihilation operator. We introduce the phase shift in one of the annihilation operators using the LC device, where, the amplitude of these operations is ultimately reduced. The alignment of an LC director is homogeneous and the director profile is calculated by solving the Euler–Lagrange equation. A total number of retardations can be calculated using the effective refractive index of the LC molecule integrating through cell thickness direction. As a result, a detail of the quantization operation is clarified.
Abstract A Mach–Zehnder interferometer with an optical phase control by a twisted nematic (TN) liquid crystal (LC) device was studied. In a typical TN LC device, a change in the optical rotation state of π/2 can be obtained by applying a voltage of about 5 V with a cell thickness of several-micron. The TN cell is inserted into one optical path in the Mach–Zehnder interferometer. We obtained a pattern change when voltage was applied to the LC cell due to the change of the optical interference state. As a result, a change in the number of photons under weak light conditions is observed.